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常见 微积分 问题
integral of (\sqrt[7]{x}+\sqrt[8]{x})
∫
(
7
√
x
+
8
√
x
)
dx
derivative 4xy^2
derivative
4
xy
2
integral of x/((1+x^4))
∫
x
(
1
+
x
4
)
dx
limit as x approaches-3 of (6-3x)(3/5 x-1)
lim
x
→
−
3
(
(
6
−
3
x
)
(
3
5
x
−
1
)
)
integral of 2y^2+ye^{xy}
∫
2
y
2
+
ye
xy
dx
(5y^2-xy)dx+(x^2)dy=0
(
5
y
2
−
xy
)
dx
+
(
x
2
)
dy
=
0
y^{''}-3y^'=8
y
′
′
−
3
y
′
=
8
(\partial)/(\partial x)(y^2e^{xyz})
∂
∂
x
(
y
2
e
xyz
)
limit as x approaches 1-of (x-2)^2
lim
x
→
1
−
(
(
x
−
2
)
2
)
(\partial)/(\partial x)(3x^2+3y^2-15)
∂
∂
x
(
3
x
2
+
3
y
2
−
1
5
)
derivative h(x)= 1/((-3x^2+3x-2)^3)
derivative
h
(
x
)
=
1
(
−
3
x
2
+
3
x
−
2
)
3
derivative 126x(9x^2+6)^6
derivative
1
2
6
x
(
9
x
2
+
6
)
6
integral of 20tan^3(x)
∫
2
0
tan
3
(
x
)
dx
integral from-1 to 0 of x+1
∫
−
1
0
x
+
1
dx
面积 y=x+1,y=7x-17,y=-2x-2
area
y
=
x
+
1
,
y
=
7
x
−
1
7
,
y
=
−
2
x
−
2
面积 y=|9x|,y=x^2-10
area
y
=
|
9
x
|
,
y
=
x
2
−
1
0
integral of (2x+1)/(x^2+4)
∫
2
x
+
1
x
2
+
4
dx
y^{''}+12y^'+24y=4381e^{2t}cos(13t)
y
′
′
+
1
2
y
′
+
2
4
y
=
4
3
8
1
e
2
t
cos
(
1
3
t
)
integral of e^xsec(e^x)
∫
e
x
sec
(
e
x
)
dx
integral of tan^5(7x)
∫
tan
5
(
7
x
)
dx
derivative of (13-x^4/3)
d
dx
(
1
3
−
x
4
3
)
integral of 1/(x(3-x))
∫
1
x
(
3
−
x
)
dx
integral of cot^5(12x)
∫
cot
5
(
1
2
x
)
dx
limit as x approaches 2x of sin(x)
lim
x
→
2
x
(
sin
(
x
)
)
derivative of (10/(x-6))
d
dx
(
1
0
x
−
6
)
f(x)= x/(x^2-x+1)
f
(
x
)
=
x
x
2
−
x
+
1
limit as x approaches 0+of x*sin(1/x)
lim
x
→
0
+
(
x
·
sin
(
1
x
)
)
(3sin(x))^'
(
3
sin
(
x
)
)
′
(\partial)/(\partial z)(e^{xyz^8})
∂
∂
z
(
e
xyz
8
)
面积 f(x)=2sin(x),g(x)=2cos(x)
area
f
(
x
)
=
2
sin
(
x
)
,
g
(
x
)
=
2
cos
(
x
)
y^{''}+2y^'+y=-4e^{-t}
y
′
′
+
2
y
′
+
y
=
−
4
e
−
t
y^{''}+9y=4xe^{(2x)},y(0)=0,y^'(0)=0
y
′
′
+
9
y
=
4
xe
(
2
x
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
limit as x approaches 0+of 5x+9
lim
x
→
0
+
(
5
x
+
9
)
integral from-2 to 1 of (x^3-3x+2)
∫
−
2
1
(
x
3
−
3
x
+
2
)
dx
(\partial)/(\partial x)((x^2)/(y^2))
∂
∂
x
(
x
2
y
2
)
integral from-1 to 2 of x/(x+2)
∫
−
1
2
x
x
+
2
dx
limit as x approaches 3 of 2x^2-3x+4
lim
x
→
3
(
2
x
2
−
3
x
+
4
)
derivative cot^2(sin(x))
derivative
cot
2
(
sin
(
x
)
)
derivative of 3x^3-5x^2+4
d
dx
(
3
x
3
−
5
x
2
+
4
)
limit as x approaches 2-of 1/(x-3)
lim
x
→
2
−
(
1
x
−
3
)
sum from n=2 to infinity of 2(-1/2)^n
∑
n
=
2
∞
2
(
−
1
2
)
n
derivative of (1+csc(x^3)/(1-cot(x^3)))
d
dx
(
1
+
csc
(
x
3
)
1
−
cot
(
x
3
)
)
integral of 1/(y-5)
∫
1
y
−
5
dy
integral of sin^3(2x)cos^4(2x)
∫
sin
3
(
2
x
)
cos
4
(
2
x
)
dx
(\partial)/(\partial x)(2xe^x-y+6x^2)
∂
∂
x
(
2
xe
x
−
y
+
6
x
2
)
integral of (x^3-3x^2+1)/(sqrt(x))
∫
x
3
−
3
x
2
+
1
√
x
dx
derivative of xi
d
dx
(
xi
)
derivative x/(2-tan(x))
derivative
x
2
−
tan
(
x
)
面积 3(x+1),4(x+1),0,3
area
3
(
x
+
1
)
,
4
(
x
+
1
)
,
0
,
3
integral of e^{-x}*e^x
∫
e
−
x
·
e
x
dx
limit as x approaches 0 of (sin(8x))/(tan(9x))
lim
x
→
0
(
sin
(
8
x
)
tan
(
9
x
)
)
integral of (sin(t))/((4+cos(t))^5)
∫
sin
(
t
)
(
4
+
cos
(
t
)
)
5
dt
integral of ((sqrt(x))/x)
∫
(
√
x
x
)
dx
面积 4x^2,6x-2
area
4
x
2
,
6
x
−
2
integral of (2x)/(1+x^2)
∫
2
x
1
+
x
2
dx
(\partial)/(\partial x)(xe^{sqrt(5xy)})
∂
∂
x
(
xe
√
5
xy
)
integral of 7xsin(x)cos(x)
∫
7
x
sin
(
x
)
cos
(
x
)
dx
derivative of x/(sqrt(x+3))
d
dx
(
x
√
x
+
3
)
limit as x approaches 0 of-x^2sin(3x)
lim
x
→
0
(
−
x
2
sin
(
3
x
)
)
inverse拉普拉斯 s/((s^2+9)(s^2+16))
inverselaplace
s
(
s
2
+
9
)
(
s
2
+
1
6
)
integral of (sqrt(x))/2
∫
√
x
2
dx
y^{''}+5y+349/4 y=0,y(0)=-5,y^'(0)=-29/2
y
′
′
+
5
y
+
3
4
9
4
y
=
0
,
y
(
0
)
=
−
5
,
y
′
(
0
)
=
−
2
9
2
derivative of (x^3+2^3)
d
dx
(
(
x
3
+
2
)
3
)
integral from-1 to 1 of x/(sqrt(x^2+25))
∫
−
1
1
x
√
x
2
+
2
5
dx
(\partial)/(\partial z)(y^2e^{xyz})
∂
∂
z
(
y
2
e
xyz
)
integral from 1 to infinity of 1/(x^2+4)
∫
1
∞
1
x
2
+
4
dx
(\partial)/(\partial x)(x^2+xy+y^2-6x+2)
∂
∂
x
(
x
2
+
xy
+
y
2
−
6
x
+
2
)
integral of (e^2x)/(4+e^4x)
∫
e
2
x
4
+
e
4
x
dx
(dy)/(dx)=((2x+1))/(2y)
dy
dx
=
(
2
x
+
1
)
2
y
derivative 9x(2x^2+1)
derivative
9
x
(
2
x
2
+
1
)
integral of (xln(x))^2(1/(x^2))
∫
(
x
ln
(
x
)
)
2
(
1
x
2
)
dx
斜率 2sqrt(x)
slope
2
√
x
integral of sqrt(9t^2+4)
∫
√
9
t
2
+
4
dt
y^'=x+y+1
y
′
=
x
+
y
+
1
derivative of (1+2x/(3-4x))
d
dx
(
1
+
2
x
3
−
4
x
)
integral of cos^n(x)
∫
cos
n
(
x
)
dx
25y^{''}+10y^'+y=0
2
5
y
′
′
+
1
0
y
′
+
y
=
0
(\partial)/(\partial x)(9/(x^2+y^2))
∂
∂
x
(
9
x
2
+
y
2
)
integral of (5x^4-6x^2+3)
∫
(
5
x
4
−
6
x
2
+
3
)
dx
integral of (e^{2x})/(4+e^{2x)}
∫
e
2
x
4
+
e
2
x
dx
derivative of ln(e^x+3)
d
dx
(
ln
(
e
x
+
3
)
)
integral of tan(9x)sec^{5/4}(9x)
∫
tan
(
9
x
)
sec
5
4
(
9
x
)
dx
limit as x approaches infinity of x^2-5
lim
x
→
∞
(
x
2
−
5
)
limit as t approaches-3 of (t-2)/(t+5)
lim
t
→
−
3
(
t
−
2
t
+
5
)
derivative ((x^2+1)/(x^2-1))^5
derivative
(
x
2
+
1
x
2
−
1
)
5
integral of (3*2^x-2*3^x)/(2x)
∫
3
·
2
x
−
2
·
3
x
2
x
dx
inverse拉普拉斯 1/(sqrt(x))
inverselaplace
1
√
x
derivative f(x)=2x^2-x
derivative
f
(
x
)
=
2
x
2
−
x
xdx+sin^2(y/x)(ydx-xdy)=0
xdx
+
sin
2
(
y
x
)
(
ydx
−
xdy
)
=
0
integral of (r^3+1)^2*r^2
∫
(
r
3
+
1
)
2
·
r
2
dr
integral of (x^4-x^3)/(x^5)
∫
x
4
−
x
3
x
5
dx
derivative of (x^3+9/x)
d
dx
(
x
3
+
9
x
)
y^'=(y^3+1)/((3xy^2))
y
′
=
y
3
+
1
(
3
xy
2
)
(\partial)/(\partial x)(3xy^2)
∂
∂
x
(
3
xy
2
)
derivative of 4x^3y^3
d
dx
(
4
x
3
y
3
)
implicit (dy)/(dx),y^4=x
implicit
dy
dx
,
y
4
=
x
(\partial)/(\partial x)(-2cos(3x))
∂
∂
x
(
−
2
cos
(
3
x
)
)
integral from 0 to 1 of 1/(1+sqrt(x))
∫
0
1
1
1
+
√
x
dx
sum from n=1 to infinity of n/(2n^4+2)
∑
n
=
1
∞
n
2
n
4
+
2
integral from 0 to 1 of e^{3sqrt(x)}
∫
0
1
e
3
√
x
dx
1
..
1413
1414
1415
1416
1417
..
2459